Convergence of a Matrix Gradient Algorithm of Solution of Extremal Problem under Constraints

摘要

A matrix regularizing algorithm of solution o an ill-posed extremal problem is proposed. This problem arises in solution of the inverse problem of radiation (field) for the linear controlled object (CO), whose mathematical model is represented by a matrix algebraic equation. Dimensions of matrices of input and output variables can be arbitrary, the matrix of CO parameters is known approximately; it can be degenerate and ill-conditioned. Sufficient conditions of asymptotic convergence of the algorithm to the matrix extremal of the smoothing functional are proved. This extremal is an approximate solution of the original extremal problem.